Is DEPC-treated water or nuclease-free water the best solvent for resuspending and storing synthesized oligos?

We recommend dissolving the stock oligo in nuclease-free HPLC grade bottled water or TE buffer (10 mM Tris pH 8.0, 0.1 mM EDTA). Use of DEPC water is strongly discouraged for several reasons:

DEPC (Diethyl Pyrocarbonate) is carcinogenic. It also has a strong affinity for adenosine, and even trace amounts will result in chemical modification of adenine residues (Henderson et al., 1973). DEPC is reactive with primary amine groups and mercaptans. In addition, DEPC should never be added to buffers that contain TRIS (tris[hydroxymethyl]aminomethane). DEPC is hard to remove, and it interferes with PCR and other reactions. (Source: RNA Methodologies, Second Edition; Robert E. Rarrell, Jr, pp 43-44.)

IDT supplies both nuclease-free water and TE. See Molecular Biology Reagents > Buffers and Solutions, on the IDT website.